Question: Simplify the following expression: $ q = 1 - \dfrac{-8z}{-7z + 10} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-7z + 10}{-7z + 10}$ $ \dfrac{1}{1} \times \dfrac{-7z + 10}{-7z + 10} = \dfrac{-7z + 10}{-7z + 10} $ Therefore $ q = \dfrac{-7z + 10}{-7z + 10} - \dfrac{-8z}{-7z + 10} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-7z + 10 + 8z }{-7z + 10} $ Distribute the negative sign: $q = \dfrac{-7z + 10 + 8z}{-7z + 10}$ $q = \dfrac{z + 10}{-7z + 10}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{-z - 10}{7z - 10}$